Comparative Study of Color Glass Condensate and Collinear Frameworks for Large-Transverse-Momentum Semi-Inclusive Deep Inelastic Scattering

Abstract: We study the Semi-Inclusive Deep Inelastic Scattering (SIDIS) cross-section at large values of hadron transverse momentum $P_t \gtrsim Q$, with $Q<sup>2$ being the photon virtuality. This kinematic regime of SIDIS allows for a collinear factorization in terms of parton distribution functions (PDFs) and collinear fragmentation functions (FFs). On the other hand, at high energies, i.e., at small Bjorken $x$, the same SIDIS process can also be factorized within the Color Glass Condensate (CGC) framework in terms of eikonal dipole amplitudes. In this work, we perform a systematic comparison of the leading-order (LO) and next-to-leading-order (NLO) collinear and the LO CGC factorizations of this process based on the COMPASS and HERA data. We further provide comparisons of these two factorization frameworks for nucleon and nuclear large-$P_t$ SIDIS in the expected Electron Ion Collider (EIC) kinematics. We find, within the present theoretical uncertainties, that it might be difficult to distinguish between these two factorization schemes for nuclear SIDIS at the EIC. We also observe a significant dependence of the LO eikonal CGC predictions on the choice of longitudinal momentum fraction $x_g$, suggesting significant beyond-eikonal corrections for the EIC kinematics.